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Stage 2. Since expert estimates are given in the form of trapezoidal fuzzy numbers, first of all, it is necessary to determine the boundaries of the scale of
6. Conclusions
The presented work aims to propose a new approach for an assessment of the credit risks under uncertainty. The novelty of the proposed approach is the use of trapezoidal fuzzy numbers, which makes it possible to adequately form and process the experts’estimates. An important fact is that the proposed approach takes into account the degrees of experts’importance.
The main results of the work are as follows:
• A brief analysis of existing models is carried out, and the feasibility of creating a new approach is justified.
• The rationale for the presentation of experts’assessments of the credit risk in the form of trapezoidal fuzzy numbers is given.
• The linguistic variable“degree of credit risk”is formed.
• A polar percentage and coordinate scales of trapezoidal fuzzy numbers with a gradation of assigned levels are defined. The formalization of the mapping of the percentage scale to the coordinate scale is given.
Figure 5.
Graphical expression of the degree of risk in percent.
• The criteria for an assessment of the credit risks are generated.
• Generalized algorithms for implementing the proposed approach are constructed.
• A toy example which illustrates the practical application of the proposed approach is provided.
Author details Teimuraz Tsabadze
Georgian Technical University, Tbilisi, Georgia
*Address all correspondence to: teimuraz.tsabadze@yahoo.com
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/
by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Banking and Finance
References
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Individual loan risk. In: Financial Institutions Management: A Risk Management Approach. NY: McGraw- Hill/Irwin; 2010. pp. 295-338
[2]Tsabadze T. Assessment of credit risk based on fuzzy relations. AIP Conference Proceedings. 2017;1836(1):020-027 [3]Zadeh LA. Fuzzy sets. Information and Control. 1965;8:338-353
[4]Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning. Information Sciences. 1975;8:
199-249. 301-357; Vol. 9, 43-80
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Fuzzy Logic - Emerging Technologies and Applications. London: InTech; 2012.
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[6]BrkićS, HodžićM, DžanićE. Soft data modeling via type 2 fuzzy distributions for corporate credit risk assessment in commercial banking. In:
Proceedings of the International Symposium on Innovative and Interdisciplinary Applications of Advanced Technologies (IAT 2018), 21–24 June. Vol. 1. Jahorina, Bosnia and Herzegovina; 2018. pp. 457-469
[7]Tsabadze T. A method for aggregation of trapezoidal fuzzy
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Boston, MA: The Handbooks of Fuzzy Sets Series, Kluwer Academic
Publishers; 2000. pp. 483-581 [9]Heilpern S. Representation and application of fuzzy numbers. Fuzzy Sets and Systems. 1997;91:259-268
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Amsterdam: Elsevier North-Holland;
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A Bipartite Graph-Based
Recommender for Crowdfunding with Sparse Data
Hongwei Wang and Shiqin Chen
Abstract
It is a common problem facing recommender to sparse data dealing, especially for crowdfunding recommendations. The collaborative filtering (CF) tends to rec- ommend a user those items only connecting to similar users directly but fails to recommend the items with indirect actions to similar users. Therefore, CF performs poorly in the case of sparse data like Kickstarter. We propose a method of enabling indirect crowdfunding campaign recommendation based on bipartite graph.
PersonalRank is applicable to calculate global similarity; as opposed to local simi- larity, for any node of the network, we use PersonalRank in an iterative manner to produce recommendation list where CF is invalid. Furthermore, we propose a bipartite graph-based CF model by combining CF and PersonalRank. The new model classifies nodes into one of the following two types: user nodes and campaign nodes. For any two types of nodes, the global similarity between them is calculated by PersonalRank. Finally, a recommendation list is generated for any node through CF algorithm. Experimental results show that the bipartite graph-based CF achieves better performance in recommendation for the extremely sparse data from
crowdfunding campaigns.
Keywords:crowdfunding, recommender, bipartite graph, network structure
1. Introduction
As the largest crowdfunding platform in the world, Kickstarter has attracted 8,604,863 users who participated in 230,850 campaigns with 22,525,091 investment behaviors (www.kickstarter.com). However, about 60% of the campaigns are unsuccessfully financed. The main reason is that many campaigns failed to find enough investors, rather than the ideas were not good enough [1]. Therefore, a recommender for crowdfunding is the key to solving this problem.
A survey has shown that the sparseness of user behaviors in Kickstarter is about 99.99%, leading to the commonly used recommendation algorithms inefficient. For example, collaborative filtering (CF) algorithm based on cosine similarity aims to find users who have the same preference, then calculates interest similarity, and produces recommendation list. However, it is difficult for the algorithm to find similar users on a sparse data, which is one of the main problems faced by recommender systems [2].
Faced with large-scale sparse data, network analysis algorithms are effective approaches to overcome the problem. For example, the PageRank algorithm is applicable to calculate the weight of web nodes. As a global iterative algorithm, PageRank does not distinguish the types of nodes, making it hard to improve the recommendation performance. However, an improved algorithm based on
PageRank (i.e., bipartite graph model) provides ideas for us. Using bipartite graph model, we divide the network into an item-user structure, where there is no direct edge between items or between users. Then, the global similarity is calculated by bipartite graph analysis, as opposed to local similarity calculated by cosine function, and can better deal with the problem of sparse data.
Experiments show that bipartite graph model can effectively produce recom- mendation lists with sparse data. Furthermore, in the global iterative process of bipartite graph model, the similarity between items or between users is also calcu- lated, in addition to the similarity between items and users. Compared with cosine function, which can only calculate adjacent users, this kind of similarity is extracted from the network, thus it is able to solve the computation problem caused by sparse data. Therefore, we propose a bipartite graph-based CF model by combining the similarity calculated by bipartite graph model with CF algorithm.
2. Literature review